30–32 = 0
33–35 = 2
36–38 = 0
39–41 = 2
42–44 = 1
45–47 = 1
48–50 = 3

Measures of Central Tendency
Sampling Distributions
The Sampling Distribution of the Mean
The Sampling Distribution of the M
Mode
The category with the most values is 48-50 with 3 values.

Measures of Central Tendency
Sampling Distributions
The Sampling Distribution of the Mean
The Sampling Distribution of the M
Mode
The category with the most values is 48-50 with 3 values.
We can take the mid value of the category to estimate the mode
at 49.

Measures of Central Tendency
Sampling Distributions
The Sampling Distribution of the Mean
The Sampling Distribution of the M
Mode
The category with the most values is 48-50 with 3 values.
We can take the mid value of the category to estimate the mode
at 49.
This method of calculating the mode is not ideal as, depending on
the categories you define, the mode may be different.

Measures of Central Tendency
Sampling Distributions
The Sampling Distribution of the Mean
The Sampling Distribution of the M
Mean, Median and Mode for Grouped Data
Example 9
The table below gives data on the heights, in cm, of 51 children.
Class Interval
Frequency
140
≤
h
<
150
6
150
≤
h
<
160
16
160
≤
h
<
170
21
170
≤
h
<
180
8
(a) Estimate the mean, (b) estimate the median and (c) find the
modal class.

Measures of Central Tendency
Sampling Distributions
The Sampling Distribution of the Mean
The Sampling Distribution of the M
Solution. (a)
To estimate the mean, the mid-point of each
interval should be used
Class Interval
Mid-point
Frequency
Mid-point
×
Frequency
140
≤
h
<
150
145
6
145
×
6 = 870
150
≤
h
<
160
155
16
155
×
16 = 2480
160
≤
h
<
170
165
21
165
×
21 = 3465
170
≤
h
<
180
175
8
175
×
8 = 1400
Totals
51
8215

Measures of Central Tendency
Sampling Distributions
The Sampling Distribution of the Mean
The Sampling Distribution of the M
Solution. (a)
To estimate the mean, the mid-point of each
interval should be used
Class Interval
Mid-point
Frequency
Mid-point
×
Frequency
140
≤
h
<
150
145
6
145
×
6 = 870
150
≤
h
<
160
155
16
155
×
16 = 2480
160
≤
h
<
170
165
21
165
×
21 = 3465
170
≤
h
<
180
175
8
175
×
8 = 1400
Totals
51
8215
Mean =
x
=
8215
51
= 161 (to the nearest cm)

Measures of Central Tendency
Sampling Distributions
The Sampling Distribution of the Mean
The Sampling Distribution of the M
(b)
the median is the 26th value. In this case it lies in the
160
≤
h
<
170 class interval. The 4th value in the interval is
needed. It is estimated as
160 +
4
21
×
10 = 162 (to the nearest cm)
.

Measures of Central Tendency
Sampling Distributions
The Sampling Distribution of the Mean
The Sampling Distribution of the M
(b)
the median is the 26th value. In this case it lies in the
160
≤
h
<
170 class interval. The 4th value in the interval is
needed. It is estimated as
160 +
4
21
×
10 = 162 (to the nearest cm)
.
(c)
The modal class is 160
≤
h
<
170 as it contains the most
values.

Measures of Central Tendency
Sampling Distributions
The Sampling Distribution of the Mean
The Sampling Distribution of the M
Note.

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- Fall '07
- Aarron
- Tendency Sampling Distributions, Central Tendency Sampling