12 Measures of Central Tendency - BrainWorks



12. Measures of Central Tendency 12.1 Mean of Ungrouped Data

Mark: ________/ 6

Find the mean of each of the following sets of data. Correct the answer to 2 decimal places if necessary. (Qn.1 – 4)

1. 14 , 16 , 10 , 11 , 13 , 14

2. 62 , 47 , 97 , 36 , 42 , 15

3. 1 , –1 , –2 , 0 , 2 , 1

4. 1.5 , –1.5 , –2.5 , 3.5 , –2.5 , –1.5

Find the mean of each of the following sets of data (Qn.5 – 6)

|5. |Data |1 |2 |3 |4 |

| |Frequency |8 |7 |10 |5 |

|6. |Data |10 |12 |15 |17 |20 |23 |

| |Frequency |3 |5 |10 |15 |15 |12 |

12. Measures of Central Tendency 12.2 Mean of Grouped Data

Mark: ________/ 4

Find the mean of each of the following sets of data. Correct the answer to 2 decimal places if necessary. (Qn.1 – 4)

|1. |Data |11 – 15 |16 – 20 |21 – 25 |26 – 30 |31 – 35 |

| |Frequency |6 |8 |11 |9 |6 |

|2. |Data |26 – 30 |31 – 35 |36 – 40 |41 – 45 |46 – 50 |

| |Frequency |30 |40 |65 |45 |20 |

|3. |Data |11 – 20 |21 – 30 |31 – 40 |41 – 50 |51 – 60 |

| |Frequency |5 |14 |17 |8 |6 |

|4. |Data |101 – 110 |111 – 120 |121 – 130 |131 – 140 |141 – 150 |

| |Frequency |40 |55 |75 |65 |45 |

12. Measures of Central Tendency 12.3 Median of Ungrouped Data

Mark: ________/ 6

Find the median of each of the following sets of data. (Qn. 1 – 6)

1. 16 , 16 , 17 , 18 , 19 , 20 , 20 , 22

2. 51 , 52 , 52 , 53 , 55 , 57 , 63

3. 26 , 21 , 22 , 22 , 24 , 19 , 20

4. 34 , 30 , 31 , 32 , 30 , 28 , 28 , 30

|5. |Data |3 |5 |7 |9 |10 |

| |Frequency |2 |3 |6 |4 |5 |

|6. |Data |15 |17 |20 |27 |32 |

| |Frequency |6 |9 |10 |11 |9 |

12. Measures of Central Tendency 12.4 Median of Grouped Data

Mark: ________/ 2

1. The following cumulative frequency polygon shows the scores of 40 students in a Chinese test.

Scores of 40 students in a Chinese test

[pic]

Score

Find the median score. (Correct the answer to the nearest integer.)

2. The following cumulative frequency polygon shows the heights of 50 students.

Heights of 50 students

[pic]

Find the median height. (Correct the answer to the nearest integer.)

12. Measures of Central Tendency 12.5 Mode of Ungrouped Data

Mark: ________/ 6

Find the mode of each of the following sets of data. (Qn. 1 – 4)

1. 6 , 7 , 6 , 8 , 8 , 8 , 9 , 7 , 8 , 9

2. 36 , 37 , 39 , 37 , 36 , 37 , 38 , 37 , 36 , 40

3. 184 , 160 , 164 , 164 , 165 , 186 , 146 , 164

4. 241 , 246 , 247 , 248 , 249 , 240 , 246 , 242 , 245 , 247 , 247

5. Find the mode of the following set of data.

|Data |21 |22 |28 |29 |31 |

|Frequency |1 |5 |8 |4 |2 |

6. The following table shows the ages of 40 students.

|Age |14 |15 |16 |17 |18 |

|Frequency |9 |17 |6 |4 |4 |

Find the mode of ages of the students.

12. Measures of Central Tendency 12.6 Mode of Grouped Data

Mark: ________/ 5

Find the modal class in each of the following distribution. (Qn. 1 – 5)

|1. |Data |1 – 5 |6 – 10 |11 – 15 |16 – 20 |21 – 25 |

| |Frequency |3 |9 |15 |6 |2 |

Modal class: ______________________

|2. |Data |51 – 60 |61 – 70 |71 – 80 |81 – 90 |91 – 100 |

| |Frequency |7 |12 |11 |8 |2 |

Modal class: ______________________

|3. |Data |11 – 20 |21 – 30 |31 – 40 |41 – 50 |51 – 60 |

| |Frequency |6 |14 |17 |8 |5 |

Modal class: ______________________

|4. |Data |121 – 130 |131 – 140 |141 – 150 |151 – 160 |161 – 170 |

| |Frequency |4 |9 |14 |16 |8 |

Modal class: ______________________

|5. |Data |2 – 4 |5 – 7 |8 – 10 |11 – 13 |14 – 16 |

| |Frequency |10 |7 |5 |6 |2 |

Modal class: ______________________

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12.2

12.1

12.3

12.4

Cumulative frequency

Cumulative frequency

12.6

12.5

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