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Approximate the median of the frequency distribution in Problem 3

Approximate the median of the frequency distribution in Problem 3.

Temperature (°F) .... Frequency

61-64 ......... 31

65-67 ......... 67

68-69 ....... 198

70 ......... 195

71-72 ........ 120

73-76 ......... 89

77-80 ......... 50

Use the following steps to approximate the median from grouped data.

Approximating the Median from Grouped Data

Step I Construct a cumulative frequency distribution.

Step 2 Identify the class in which the median lies. Remember, the median can be obtained by determining the observation that lies in the middle.

Step 3 Interpolate the median using the formula

where

L is the lower class limit of the class containing the median

n is the number of data values in the frequency distribution

CF is the cumulative frequency of the class immediately preceding the class containing the median

f is the frequency of the median class

i is the class width of the class containing the median

Temperature (°F) .... Frequency

61-64 ......... 31

65-67 ......... 67

68-69 ....... 198

70 ......... 195

71-72 ........ 120

73-76 ......... 89

77-80 ......... 50

Use the following steps to approximate the median from grouped data.

Approximating the Median from Grouped Data

Step I Construct a cumulative frequency distribution.

Step 2 Identify the class in which the median lies. Remember, the median can be obtained by determining the observation that lies in the middle.

Step 3 Interpolate the median using the formula

where

L is the lower class limit of the class containing the median

n is the number of data values in the frequency distribution

CF is the cumulative frequency of the class immediately preceding the class containing the median

f is the frequency of the median class

i is the class width of the class containing the median

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