Find the mean, median, and mode for each of the following data sets:
1) 91, 92, 93, 92, 95
2) 2, 4, 4
3) 51, 56, 51, 57, 54, 65
4) 9, 10, 11
5) 41, 42, 43, 44, 44
Answer (2)
The calculations for each data set reveal the mean, median, and mode: 1) Mean 92.6, Median 92, Mode 92; 2) Mean ≈ 3.33, Median 4, Mode 4; 3) Mean ≈ 55.67, Median 55, Mode 51; 4) Mean 10, Median 10; No mode; 5) Mean 42.8, Median 43, Mode 44.
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To find the mean, median, and mode for each of the given data sets, follow the definitions and steps for each measure of central tendency.
Data Set: 91 , 92 , 93 , 92 , 95
Mean: The mean is the average of a set of numbers. Add all the numbers together, then divide by the number of values: Mean = 5 91 + 92 + 93 + 92 + 95 = 5 463 = 92.6
Median: The median is the middle value when the numbers are arranged in ascending order. Arrange the numbers: 91 , 92 , 92 , 93 , 95 . The middle value is 92 .
Mode: The mode is the number that appears most frequently. Here, 92 appears twice, so the mode is 92 .
Data Set: 2 , 4 , 43
Mean: Mean = 3 2 + 4 + 43 = 3 49 ≈ 16.33
Median: Arrange the numbers: 2 , 4 , 43 . The middle value is 4 .
Mode: There is no repeating number, so this data set has no mode.
Data Set: 51 , 56 , 51 , 57 , 54 , 65
Mean: Mean = 6 51 + 56 + 51 + 57 + 54 + 65 = 6 334 ≈ 55.67
Median: Arrange the numbers: 51 , 51 , 54 , 56 , 57 , 65 . The middle values are 54 and 56 . The median is: Median = 2 54 + 56 = 55
Mode: The number 51 appears twice, so the mode is 51 .
Data Set: 9 , 10 , 11
Mean: Mean = 3 9 + 10 + 11 = 3 30 = 10
Median: Arrange the numbers: 9 , 10 , 11 . The middle value is 10 .
Mode: There is no repeating number, so this data set has no mode.
Data Set: 41 , 42 , 43 , 44 , 44
Mean: Mean = 5 41 + 42 + 43 + 44 + 44 = 5 214 = 42.8
Median: Arrange the numbers: 41 , 42 , 43 , 44 , 44 . The middle value is 43 .
Mode: The number 44 appears twice, so the mode is 44 .
