Standard Deviation and Variation Notes

Standard Deviation and Variation

Aim: Calculate the standard deviation of a data set to describe the variation of the data.
Using a box and whisker plot, identify the values: minX, Q1, Med, Q3, maxX.
Create a box plot for the data: 65, 75, 92, 84, 62, 96, 88, 79, 82.

Two data sets can have the same mean, median, and mode but appear very different due to the variation within the sets.
Focus on understanding variation.

Standard Deviation: On average, it shows how far away a data point is from the mean of the data set.
A small standard deviation means the data points tend to be very close to the mean (more consistent data).
A large standard deviation means the values are more spread out.

Use a calculator to find the standard deviation (Sx) of the two data sets.
Round answers to the nearest tenth.
- Data Set #1: 3, 3, 4, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 11
- Data Set #2: 5, 5, 6, 6, 7, 7, 8, 8, 9, 9
The data set with a larger standard deviation has more spread out data.

A farm studies the weight of baby chickens after one week.
The weights (in ounces) of 20 chicks are:
- 2, 1, 3, 4, 2, 2, 3, 1, 5, 3, 4, 4, 5, 6, 3, 8, 5, 4, 6, 3
Find the mean, interquartile range, and standard deviation.
Round the answers to the nearest tenth and include units.

A marketing company studies diversity in the age of soft drink consumers.
Ages of people who prefer Soda A:
- 16, 16, 18, 18, 21, 22, 22, 25, 27, 28, 29, 36, 38, 40, 44
Ages of people who prefer Soda B:
- 18, 18, 19, 19, 20, 22, 22, 23, 25, 25, 26, 27, 28, 29, 30
(a) Explain why standard deviation is better than the mean for measuring age diversity.
(b) Determine which soda has greater age diversity and explain the choice.
(c) Use a calculator to find the sample standard deviation (Sx) for both data sets and round to the nearest tenth. Check if this result supports the choice from (b).

Which data set has a standard deviation closest to zero? (Answer without a calculator.)
- (1) {-5, -2, -1, 0, 1, 2, 5}
- (2) {5, 8, 10, 16, 20}
- (3) {11, 11, 12, 13, 13}
- (4) {3, 7, 11, 11, 11, 18}

Home run data for the 16 batters with the most home runs in the 2005 MLB season:
- 51, 48, 47, 46, 45, 43, 41, 40, 40, 39, 42, 44, 46, 48, 49, 38
Identify values for the data set.

Use your calculator to find the interquartile range (IQR) and sample standard deviation (Sx).
- Show the calculation for the IQR. Round non-integer values to the nearest tenth.
- (a) 4, 6, 8, 10, 15, 19, 22, 25
- (b) 3, 3, 4, 5, 5, 6, 6, 7, 7, 8
Given a dot plot, determine the closest population standard deviation (σx).
What is the IQR of the data set represented in the box plot?
Which measure best represents the average distance of a data value from the mean?
Which data set has the largest standard deviation?

Use calc. to get Five-Number Summary: Min, Q1, Med, Q3, Max
1. Enter data in L₁ (STAT -1: Edit…)
2. STAT > CALC 1: 1-Var Stats
3. Enter 3x
IQR = Q3-Q1