Name: _________________
AP Statistics Handout: Lesson 1.4
Topics: measures of center, measures of spread, using technology to find summary stats
Lesson 1.4 Guided Notes
Measures of Center
Mean:
𝑥̅ =
𝑥̅ =
𝑛
=
∑ 𝑥𝑖
𝑛
39 + 34 + 34 + 35 + 34 + 32 + 43 + 34 + 185 + 35 + 29 + 67 601
=
= _______
12
12
Median:
Show the steps to finding the median:
29, 32, 34, 34, 34, 34, 35, 35, 39, 43, 67, 185
Salaries
(thousands of $)
39
34
34
35
34
32
43
34
185
35
29
67
Question Preview (for later discussion): The boss is trying to hire you to work at this company. She says,
“Our typical salary is $50,100.” Is this misleading? Why or why not?
Approximating a median in a histogram: The graph below describes 55 ACT scores.
1. Divide the sample size (the total number of
data points) by 2. This is the ______________
of the ____________ value of the dataset –
the median.
2. From the lowest value datapoints, count
the ________________ until you reach the
central position from step #1.
3. Report the _____________ of possible
values for the median.
Material adapted from the Skew The Script curriculum (skewthescript.org)
Lessons made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License
(https://creativecommons.org/licenses/by-nc-sa/4.0)
2
Measures of Spread
Range:
Range = Max – Min
Range = 185 – 29 = _____
Standard Deviation:
𝒔𝒙 = 𝟒𝟑. 𝟔𝟏
The salaries in the dataset are typically
$43,610 _______________ the mean.
∑(𝑥𝑖 − 𝑥̅ )2
𝑠𝑥 = √
𝑛−1
Interquartile Range (IQR):
Show the steps to finding the interquartile range (IQR):
Formula: IQR = Q3 – Q1
29, 32, 34, 34, 34, 34, 35, 35, 39, 43, 67, 185
Question Preview (for later discussion): Which measure of spread (range, standard dev., or IQR) best
represents the “typical” distance between salaries? Why?
Material adapted from the Skew The Script curriculum (skewthescript.org)
Lessons made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License
(https://creativecommons.org/licenses/by-nc-sa/4.0)