Question 17·Medium·One-Variable Data Distributions; Measures of Center and Spread
A start-up tracked the number of new users who signed up each day for two consecutive months. The summary statistics are shown in the table.
| Month | Sample size (days) | Mean (new users per day) | Standard deviation (new users per day) |
|---|---|---|---|
| April | 30 | 140 | 16 |
| May | 31 | 140 | 22 |
Which statement is supported by the information in the table?
For questions about one-variable data summaries, first identify which statistics are actually provided (mean, standard deviation, sample size, etc.). Recall what each measure tells you: mean for center, standard deviation and interquartile range for spread. Then quickly eliminate any answer choices that talk about statistics you do not have (like quartiles, medians, or maximums) or that require the raw data. Finally, compare the relevant measures (such as which standard deviation is larger) and choose the statement that directly matches that comparison.
Hints
Focus on what is actually given
Look carefully at the columns in the table. Which measures of center and spread are provided, and which are not provided?
Think about what standard deviation means
Standard deviation describes how spread out the data values are around the mean. If one month has a larger standard deviation than the other, what does that tell you about the day-to-day changes?
Check which choices use information you actually have
Some answer choices mention things like the interquartile range, the median, or the largest value. Do you see any of those values or enough information to calculate them in the table?
Compare the two months using the spread
The means are equal, but the standard deviations are different. Use that difference to decide which month has more variation from day to day, and then pick the statement that matches that idea.
Desmos Guide
Compare the standard deviations numerically
In Desmos, type 22 and 16 (the standard deviations for May and April). You can also type 22 - 16 or 22 > 16 to see which is larger. Use this comparison to decide which month has more variation in daily sign-ups.
Step-by-step Explanation
Read the key statistics in the table
From the table:
- April: sample size , mean , standard deviation .
- May: sample size , mean , standard deviation .
So both months have the same mean, but different standard deviations.
Recall what mean and standard deviation tell you
- The mean is the average daily sign-up count.
- The standard deviation measures how spread out the daily counts are around the mean.
- A larger standard deviation means more variation (data points are, on average, farther from the mean).
- A smaller standard deviation means less variation (data points are closer to the mean).
Compare the spread (variation) for April and May
Compare the standard deviations:
- April: standard deviation
- May: standard deviation
Since , the daily user sign-up numbers in May are more spread out around 140 than those in April. That means the May data have greater variability.
Now think about the answer choices: only one talks directly about variation in a way that we can confirm using the standard deviation. The others talk about things like interquartile range, median, or maximum, which are not given in the table.
Match this conclusion to the correct statement
Because May has a larger standard deviation than April, the daily sign-up numbers in May varied more from day to day than those in April.
Therefore, the supported statement is:
The daily sign-up numbers in May varied more than those in April.