# Measures of Central Tendency

Calculate and label the sample sum, n, mode, median, and mean (show your work)

Data set #1: 27, 65, 61, 15, 71, 41, 11, 2, 7, 15, 39, 16, 27, 39, 10

Sum

Sum, 27 + 65 + 61 + 15 + 71 + 41 + 11 + 2 + 7 + 15 + 39 + 16 + 27 + 39 + 10

= 446

Sample size, n

The sample size, n

There are fifteen samples, thus, n = 15

Mode

The mode is a measure of central tendency referring to data value with the highest frequency.

27, 65, 61, 15, 71, 41, 11, 2, 7, 15, 39, 16, 27, 39, 10

Step I: Arranging the data set in ascending order

2, 7, 10, 11, 15, 15, 16, 27, 27, 39, 39, 41, 61, 65, 71

Step II: Identifying the most recurring value(s)

 Value Frequency 2 1 7 1 10 1 11 1 15 2 16 1 27 2 39 2 41 1 61 1 65 1 71 1

The values with the highest frequency are 15, 27 and 39 with each occurring twice. Therefore, the Mode of the data set is 15, 27, and 39.

This phenomenon, where there are three modes in a data set, is known as trimodal.

Median

Median is a measure of central tendency referring to the center-most data value.

27, 65, 61, 15, 71, 41, 11, 2, 7, 15, 39, 16, 27, 39, 10

Step I: Arranging the data set in ascending order

2, 7, 10, 11, 15, 15, 16, 27, 27, 39, 39, 41, 61, 65, 71

Step II: Identifying the center-most value

In the data set 2, 7, 10, 11, 15, 15, 16, 27, 27, 39, 39, 41, 61, 65, 71, the central value is 27

Thus, Mode = 27

Mean

Mean is the sum of all data sets divided by the total number of species.

Data set #2: 75, 18, 64, 35, 16, 97, 65, 79, 19, 4, 15, 3, 75, 58, 9

Sum

Sum, 75 + 18 + 64 + 35 + 16 + 97 + 65 + 79 + 19 + 4 + 15 + 3 + 75 + 58 + 9

= 632

The sample size, n

The sample size, n

There are fifteen samples, thus, n = 15

Mode

The mode is a measure of central tendency referring to data value with the highest frequency.

75, 18, 64, 35, 16, 97, 65, 79, 19, 4, 15, 3, 75, 58, 9

Step I: Arranging the data set in ascending order

3, 4, 9, 15, 16, 18, 19, 35, 58, 64, 65, 75, 75, 79, 97

Step II: Identifying the most recurring value(s)

 Value Frequency 3 1 4 1 9 1 15 1 16 1 18 1 19 1 35 1 58 1 64 1 65 1 75 2 79 1 97 1

The value with the highest frequency is 75, and it occurs twice. Therefore, the Mode of the data set is 75.

Median

Median is a measure of central tendency referring to the center-most data value.

75, 18, 64, 35, 16, 97, 65, 79, 19, 4, 15, 3, 75, 58, 9

Step I: Arranging the data set in ascending order

3, 4, 9, 15, 16, 18, 19, 35, 58, 64, 65, 75, 75, 79, 97

Step II: Identifying the center-most value

In the data set 3, 4, 9, 15, 16, 18, 19, 35, 58, 64, 65, 75, 75, 79, 97, the central value is 35

Thus, Median = 35

Mean

Mean is the sum of all data sets divided by the total number of species.

Data set #3: 16, 45, 60, 25, 11, 37, 13, 4, 12, 25,

Sum

Sum, 16 + 45 + 60 + 25 + 11 + 37 + 13 + 4 + 12 + 25

= 248

The sample size, n

The sample size, n

There are fifteen samples, thus, n = 10

Mode

The mode is a measure of central tendency referring to data value with the highest frequency.

16, 45, 60, 25, 11, 37, 13, 4, 12, 25,

Step I: Arranging the data set in ascending order

4, 11, 12, 13, 16, 25, 25, 37, 45, 60

Step II: Identifying the most recurring value(s)

 Value Frequency 4 1 11 1 12 1 13 1 16 1 25 2 37 1 45 1 60 1

The values with the highest frequency are 25 which occurs twice. Therefore, the Mode of the data set is 25.

Median

Median is a measure of central tendency referring to the center-most data value.

16, 45, 60, 25, 11, 37, 13, 4, 12, 25,

Step I: Arranging the data set in ascending order

4, 11, 12, 13, 16, 25, 25, 37, 45, 60

Step II: Identifying the center-most value

In the data set 4, 11, 12, 13, 16, 25, 25, 37, 45, 60 the central values are 16 and 25

Thus, Median =

Mean

Mean is the sum of all data sets divided by the total number of species.

Data set #4: 38, 93, 38, 6, 9, 48, 29, 24, 13, 77, 49, 93, 48

Sum

Sum, 38 + 93 + 38 + 6 + 9 + 48 + 29 + 24 + 13 + 77 + 49 + 93 + 48

= 565

The sample size, n

The sample size, n

There are fifteen samples, thus, n = 13

Mode

The mode is a measure of central tendency referring to data value with the highest frequency.

38, 93, 38, 6, 9, 48, 29, 24, 13, 77, 49, 93, 48

Step I: Arranging the data set in ascending order

6, 9, 13, 24, 29, 38, 38, 48, 48, 49, 77, 93, 93

Step II: Identifying the most recurring value(s)

 Value Frequency 6 1 9 1 13 1 24 1 29 1 38 2 48 2 49 1 77 1 93 2

The values with the highest frequency are: 38, 48 and 93 each of them occurring twice. Therefore, the Mode of the data set is 38, 48 and 93 and thus the data set is trimodal.

Median

Median is a measure of central tendency referring to the center-most data value.

38, 93, 38, 6, 9, 48, 29, 24, 13, 77, 49, 93, 48

Step I: Arranging the data set in ascending order

6, 9, 13, 24, 29, 38, 38, 48, 48, 49, 77, 93, 93

Step II: Identifying the center-most value

In the data set 6, 9, 13, 24, 29, 38, 38, 48, 48, 49, 77, 93, 93 the central value is 38

Thus, Median

Mean

Mean is the sum of all data sets divided by the total number of species.