AChor/MBF3C Name: _______________________
Date: ________________________
Worksheet 8-6: Measures of Spread
Measures of central tendency are values around which a set of data tends to cluster. However, to
analyze a set of data, it is useful to know how spread out the data are. Measures of spread
describe how the values in a set of data are distributed. Several quantities can be used to measure
the spread in a set of data.
Common Measures of Spread:
▪ Range
The range is the difference between the greatest and least values in a set of data. To calculate
the range, subtract the least value from the greatest value.
Range = Greatest value – Least value
▪ Variance
The variance is a measure of how spread out the values in a set of data are from the mean. It
is the average of the squares of the deviations from the mean for a set of data.
Note: The greater the variance, the greater the spread of the data values
( x1 mean ) 2 ( x2 mean ) 2 ( x3 mean ) 2 ... ( xn mean ) 2
Variance
n
where x1 , x 2 , x3 ,..., x n are values in the set of data ( x1 is the first value, x 2 is the second
value and so on, until x n which is the nth value or the last value), and n is the number of
values in the set of data
▪ Standard Deviation
The standard deviation is another measure of how spread out the values in a set of data are
from the mean. It is the typical distance of a particular value from the mean.
Note: The greater the standard deviation, the greater the spread of the data values
Standard Deviation Variance
▪ Quartiles
Quartiles are three values that divide a set of data into four intervals with equal numbers of
data. First Quartile is the median of the first half of the data, Second Quartile is the median of
the entire set of data, Third Quartile is the median of the second half of the data.
▪ Interquartile Range
Interquartile range measures how closely data clusters around the median. It is the range of
the central half of a set of data when the data are arranged from least to greatest.The
interquartile range is the difference between the upper quartile and the lower quartile.
Interquartile Range = Third Quartile – First Quartile
Assigned Work: WS 8-6; p. 145 #1, #5-6 (c to d), #7-8
AChor/MBF3C Name: _______________________ WS 8-6
Date: ________________________
1. Iris works part-time selling cell phones. She recorded the numbers of cell phones she sold
each month for the last 12 months: 51, 17, 25, 39, 7, 49, 62, 41, 20, 6, 43, 13.
(a) Find the median.
(b) Find the first quartile (Q1).
(c) Find the third quartile (Q3).
(d) Find the interquartile range.
2. Carmella’s monthly gasoline expenses, in dollars, for the past year are shown.
61, 83, 77, 88, 67, 71, 65, 72, 67, 84, 90, 80
(a) Calculate the range, to the nearest dollar.
(b) Calculate the variance, to the nearest dollar.
(c) Calculate the standard deviation, to the nearest dollar.
AChor/MBF3C Name: _______________________ WS 8-6
Date: ________________________
3. This set of data shows the numbers of customers who made purchases at a coffee shop each
day in one month.
114, 142, 59, 122, 111, 128, 158, 79, 88, 107, 133,
131, 113, 152, 149, 99, 84, 112, 104, 109, 122,
131, 144, 155, 139, 142, 119, 80, 127, 140, 135
(a) Find the median for the set of data.
(b) Find the first quartile.
(c) Find the third quartile.
(d) What is the interquartile range?
4. A set of data has a range of 30. The least value in the set of data is 22. What is the greatest
value in the set of data?
AChor/MBF3C Name: _______________________ WS 8-6
Date: ________________________
5. Find the range of each set of data.
(a) the number of hours worked by the restaurant staff in a given week:
11, 4, 55, 42, 41, 36, 50, 6, 8, 44, 39
(b) the number of songs Jermaine downloaded each month:
12, 11, 9, 12, 13, 15, 14, 11, 11, 8, 6, 7
6. A set of data has a range of 14. The greatest value in the set is 116. What is the least value in the
set of data?
7. Each measurement is the variance for a set of data. Find the standard deviation for each set of data.
Round your answers to one decimal place, if necessary.
(a) 154 g (b) 36 m
8. Each measurement is the standard deviation for a set of data. Find the variance for each set of data.
(a) 14.1 cm (b) 3.5 kg
AChor/MBF3C Name: _______________________ WS 8-6
Date: ________________________
9. Andrew is still working with the attendance figures, in thousands of people, for the fall fair
over the past 20 years. The data, in thousands, are:
23, 31, 44, 27, 32, 41, 35, 42, 37, 41, 43, 39, 36, 37, 43, 27, 36, 42, 41, 43
(a) Find the range.
(b) Find the variance.
(c) Find the standard deviation.
Answers: 1. (a) 32 phones, (b) 15 phones, (c) 46 phones, (d) 31 phones; 2. (a) $29, (b) $85 (Mean = $75), (c) $9;
3. (a) 122, (b) 107, (c) 140, (d) 33; 4. 52; 5. (a) 51 hours, (b) 9 songs; 6. 102; 7. (a) 12.4 g, (b) 6 m;
8. (a) 198.81 cm, (b) 12.25 kg; 9. (a) 21 000, (b) 36 100 000, (c) 6008.
