TCAP High School (EOC courses) Statistics and Probability Practice

TCAP High School (EOC courses) Statistics and Probability. Practice it free.

Summarize, represent, and interpret data; make inferences and justify conclusions from sample surveys, experiments, and observational studies; understand conditional probability and use probability to make decisions. This High School (EOC courses) reporting domain maps to 10 practice skills and 8 representative questions from the playable bank.

High School (EOC courses)10 mapped skills

Statistics and Probability skills

HSS.ID.1 Represent data with plots on the real number line and in histograms, box plots, and dot plots

HSS.ID.2 Use statistics appropriate to the shape of the data distribution to compare center and spread

HSS.ID.3 Interpret differences in shape, center, and spread in the context of the data sets

HSS.ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution

HSS.ID.5 Summarize categorical data for two categories in a two-way frequency table

HSS.IC.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population

HSS.IC.2 Decide if a specified model is consistent with results from a given data-generating process

HSS.IC.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies

HSS.CP.1 Describe events as subsets of a sample space

HSS.CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities

HSS.CP.3 Understand conditional probability and independence

HSS.CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified

HSS.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations

HSS.MD.1 Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space

HSS.MD.2 Calculate the expected value of a random variable

HSS.MD.3 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated

HSS.MD.4 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically

HSS.MD.5 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values

HSS.MD.6 Use probability to evaluate outcomes of decisions

Standards basis

Tennessee Academic Standards for Mathematics — Tennessee

How the TCAP reports it

TCAP math is Tennessee’s state assessment program and its blueprints are aligned to Tennessee Academic Standards, which closely mirror the Common Core content structure in grades 3-8 and the CCSS-style high school conceptual categories. The blueprint page lists the current 2025-26 assessment overviews, including Math Grade 2, Grades 3-5, Grades 6-8, and Math EOC. [Tennessee Department of Education](https://www.tn.gov/education/districts/lea-operations/assessment/tcap-blueprints.html)

Blueprint & weighting

Published TCAP math blueprints assign content emphasis by grade/course, but the exact percentage table was not recoverable from the accessible blueprint page in this session. The state blueprint landing page confirms the math overviews but did not expose the PDF links in the fetched page content. [Tennessee Department of Education](https://www.tn.gov/education/districts/lea-operations/assessment/tcap-blueprints.html)

Official sources

Tennessee Department of Education TCAP Blueprints
Tennessee Education Glossary (academic standards entry)

8 free questions · 0/0 correct

Practice playeasy

Four data sets show daily high temperatures (in °F). Which set has the greatest standard deviation?

Set A: $20, 22, 24, 26$
Set B: $21, 23, 25, 27, 29$
Set C: $10, 22, 24, 26, 28$
Set D: $22, 23, 24, 25, 26$

Set C includes the outlier $10$ while the other values cluster near $24$ , so values are far from the mean $22$ . Its standard deviation is about $6.3$ , greater than the evenly spaced sets A, B, and D.

Practice playeasy

Seven morning temperatures, in degrees Fahrenheit, are $62\textsf{,}$ $64\textsf{,}$ $66\textsf{,}$ $75\textsf{,}$ $70\textsf{,}$ $72\textsf{,}$ and $67\textsf{.}$ Which data set has the same mean?

The original mean is $\dfrac{62 + 64 + 66 + 75 + 70 + 72 + 67}{7} = 68$ . The set $60\textsf{,}$ $64\textsf{,}$ $66\textsf{,}$ $68\textsf{,}$ $70\textsf{,}$ $72\textsf{,}$ $76$ also has mean $68$ , so the means match.

Practice playeasy

Seven test scores are $90\textsf{,}$ $50\textsf{,}$ $80\textsf{,}$ $55\textsf{,}$ $72\textsf{,}$ $60\textsf{,}$ and $83\textsf{.}$ Which data set has the same median?

In order, the original values have middle value $72$ , so the median is $72$ . The set $49\textsf{,}$ $54\textsf{,}$ $70\textsf{,}$ $72\textsf{,}$ $96\textsf{,}$ $97\textsf{,}$ $98$ also has median $72$ , so the medians match.

Practice playeasy

From a table, 6 are defective AND from line A and 15 total are items from line A. Find the conditional probability of defective given line A (simplified fraction).

$P(A\mid B) = \dfrac{P(A \text{ and } B)}{P(B)} = \dfrac{6}{15} = \dfrac{2}{5}$ .

Practice playeasy

One spin of a prize wheel pays $\text{\char36}6$ , $\text{\char36}2$ , or nothing. Winning $\text{\char36}6$ is $5$ times as likely as winning $\text{\char36}2$ , and winning nothing is equally likely as winning $\text{\char36}2$ . What is the expected payout?

Weights are $5$ , $1$ , and $1$ (total $7$ ), so probabilities are $\dfrac{5}{7}$ , $\dfrac{1}{7}$ , and $\dfrac{1}{7}$ . Then $E = \sum p_i v_i$ , which means the sum of each probability times its value: $E = \dfrac{5}{7}(6) + \dfrac{1}{7}(2) + \dfrac{1}{7}(0) = \dfrac{32}{7} \approx \text{\char36}4.57$ .

Practice playeasy

A musician practiced piano for $40$ , $55$ , and $50$ minutes on three days. On a fourth day, the practice time was $x$ minutes. The mean practice time over the four days is $48$ minutes. What is the value of $x$ ?

Four days with a mean of $48$ minutes total $4 \times 48 = 192$ . Since $40 + 55 + 50 = 145$ , $x = 192 - 145 = 47$ .

Practice playeasy

A dot plot of the number of siblings shows 2 dots above 0, 6 dots above 1, 3 dots above 2, and 1 dot above 3. Which number of siblings occurs most often?

The tallest column ( $6$ dots) sits above $1$ , so $1$ sibling occurs most often.

Practice playeasy

A STEM fair demo uses a marble run with a fixed-width divider panel at the bottom. Four exit lanes (W, X, Y, and Z) should each receive marbles equally often. After $250$ runs, the counts were:

| Lane | Marbles |
| :-- | --: |
| W | $49$ |
| X | $57$ |
| Y | $57$ |
| Z | $87$ |

Which change would most likely make the marble run fair?

Four equal lanes should each receive about $\dfrac{250}{4}=62.5$ marbles ( $25\%$ ). Lane Z received $87$ marbles ( $34.8\%$ ), so its opening is too wide, and lane W received only $49$ marbles ( $19.6\%$ ), so its opening is too narrow. Narrowing lane Z while widening lane W shifts marble flow from the over-used lane to the under-used one on the shared divider panel.

TCAP High School (EOC courses) Statistics and Probability. Practice it free.

Statistics and Probability skills

HSS.ID.1 Represent data with plots on the real number line and in histograms, box plots, and dot plots

HSS.ID.2 Use statistics appropriate to the shape of the data distribution to compare center and spread

HSS.ID.3 Interpret differences in shape, center, and spread in the context of the data sets

HSS.ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution

HSS.ID.5 Summarize categorical data for two categories in a two-way frequency table

HSS.IC.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population

HSS.IC.2 Decide if a specified model is consistent with results from a given data-generating process

HSS.IC.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies

HSS.CP.1 Describe events as subsets of a sample space

HSS.CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities

HSS.CP.3 Understand conditional probability and independence

HSS.CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified

HSS.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations

HSS.MD.1 Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space

HSS.MD.2 Calculate the expected value of a random variable

HSS.MD.3 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated

HSS.MD.4 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically

HSS.MD.5 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values

HSS.MD.6 Use probability to evaluate outcomes of decisions

Topics mapped to this domain

Compare standard deviation of data sets (ACT)

Comparing means

Comparing medians

Conditional probability

Expected value from probability (ACT)

Find score from mean

Interpreting data displays

Make devices fair from experimental results

Normal distribution basics

Statistics basics

8 free questions · 0/0 correct

Turn statistics and probability into game time.

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