OSTP Grade 11 CCRA Statistics and Probability Practice

Practice playeasy

A survey recorded the number of text messages sent per day. Which group has the greatest standard deviation?

Group A: $50, 50, 50, 50, 50$
Group B: $40, 45, 50, 55, 60$
Group C: $48, 49, 50, 51, 52$
Group D: $30, 50, 50, 50, 70$

Group D has mean $50$ with values $30$ and $70$ each $20$ away from the center while three values sit at the mean, giving a standard deviation of about $12.6$ . Groups B and C spread less; Group A has zero spread.

Practice playeasy

The practice times, in minutes, for five days are $18\textsf{,}$ $22\textsf{,}$ $30\textsf{,}$ $20\textsf{,}$ and $35\textsf{.}$ Which data set has the same mean?

The original mean is $\dfrac{18 + 22 + 30 + 20 + 35}{5} = 25$ . The set $15\textsf{,}$ $20\textsf{,}$ $25\textsf{,}$ $30\textsf{,}$ $35$ also has mean $25$ , so the means match.

Practice playeasy

Five quiz scores are $92\textsf{,}$ $68\textsf{,}$ $75\textsf{,}$ $88\textsf{,}$ and $77\textsf{.}$ Which data set has the same median?

In order, the original values have middle value $77$ , so the median is $77$ . The set $70\textsf{,}$ $73\textsf{,}$ $77\textsf{,}$ $91\textsf{,}$ $97$ also has median $77$ , so the medians match.

Practice playeasy

In a class, $12$ students play soccer, and $9$ of those soccer players also play chess. A soccer player is picked at random. What is the probability that they also play chess?

Condition on the soccer players: $P(\text{chess}\mid\text{soccer}) = \dfrac{9}{12} = \dfrac{3}{4}$ .

Practice playeasy

During a fitness challenge, four teammates completed $15$ , $20$ , $18$ , and $22$ push-ups in the first four rounds. In the fifth round, one teammate completed $x$ push-ups. The mean number of push-ups per round is $19$ . What is the value of $x$ ?

Five rounds with a mean of $19$ push-ups total $5 \times 19 = 95$ . Since $15 + 20 + 18 + 22 = 75$ , $x = 95 - 75 = 20$ .

Practice playeasy

A science lab uses a random molecule selector. A fixed-width release bar is divided into $4$ chamber gates that should release molecules equally often. After $500$ selections, the counts were:

| Chamber | Selections |
| :-- | --: |
| A | $128$ |
| B | $82$ |
| C | $127$ |
| D | $163$ |

Which change would most likely make the selector fair?

Four equal gates should each release about $\dfrac{500}{4}=125$ times ( $25\%$ ). Chamber B was selected only $82$ times ( $16.4\%$ ), so its gate is too narrow, and chamber D was selected $163$ times ( $32.6\%$ ), so its gate is too wide. Widening the gate for chamber B by narrowing the gate for chamber D shifts release space from the over-used chamber to the under-used one on the shared release bar.

Practice playmedium

A grocer surveyed $25$ customers selected at random and found that $15$ of them purchased at least one organic item. Based on the survey, which of the following is the best estimate of the number of customers out of $500$ who would purchase at least one organic item?

The sample proportion is $\dfrac{15}{25} = \dfrac{3}{5}$ . The best estimate for $500$ customers is $\dfrac{3}{5} \times 500 = 300$ customers.

Practice playeasy

Find the mean of $5, 10, 15$ .

Mean $= \dfrac{5 + 10 + 15}{3} = \dfrac{30}{3} = 10$ .

OSTP Grade 11 CCRA Statistics and Probability. Practice it free.

Statistics and Probability skills

summarize and display data

interpret models

conditional probability

inferential reasoning

use statistics to make decisions

Topics mapped to this domain

Compare standard deviation of data sets (ACT)

Comparing means

Comparing medians

Conditional probability

Find score from mean

Make devices fair from experimental results

Problem solving in context (SAT)

Statistics basics

Interpreting data displays

Two-event conditional probability word problems (SAT)

8 free questions · 0/0 correct

Turn statistics and probability into game time.

More Grade 11 CCRA domains