Central Tendency of grouped data Statistics

Statistics

1. Central Tendency of Grouped Data Bulanadi, Niña Stephanie C. MEM – Section B

2. Central Tendency “the statistical measure that identifies a single value as representative of an entire distribution.” It aims to provide an accurate description of the entire data. Grouped Data data formed by aggregating individual observations of a variable into groups. arranged into frequency distribution.

3. Mean It is computed by adding all the values in the data set divided by the number of observations in it.   where: - Mean - frequency - class mark - total frequency        

4. Median is the middle value of the given list of data when arranged in an order   where: - Median - frequency of median class - lower boundaries of median class - class width - total frequencies - cumulative frequency before / preceding the median class            

5. Mode is the middle value of the given list of data when arranged in an order   where: - Mode - lower boundaries of modal class - difference of the frequency of the modal class and class preceding it. - difference of the frequency of the modal class and class succeeding it. - class width          

6. Based on the grouped data below, Time to travel to work No. of employees 0-9 mins 14 10-19 mins 26 20-29 mins 64 30-39 mins 46 40-49 mins 28 50-59 mins 16 60-69 mins 8 70-79 mins 4 a. Find mean, median and mode. b. Negotiations are under consideration for payment for travelling time to work. State, giving reasons, which measure of central tendency you would use if you are (1) the employer, and (2) a trade union representing the employees.

7. Time to travel to work (class) No. of employees (f) Class mark (x) (UC+LC)/2 fx Lower Boundary (LC-0.5) < cf (preceding frequency + succeeding frequency) 0-9 mins 14 (9+0)/2 = 4.5 63 -0.5 14 10-19 mins 26 (10+19)/2 = 14.5 377 9.5 40 20-29 mins 64 (20+29)/2 = 24.5 1568 19.5 104 30-39 mins 46 (30+39)/2 = 34.5 1587 29.5 150 40-49 mins 28 (40+49)/2 = 44.5 1246 39.5 178 50-59 mins 16 (50+59)/2 = 54.5 872 49.5 194 60-69 mins 8 (60+69)/2 = 64.5 516 59.5 202 70-79 mins 4 (70+79)/1 = 74.5 298 69.5 206 Lower Class (LC) Upper Class (UC) = 6527   n= 206 C = Upper Boundary – Lower Boundary C = (9+0.5)-(0-0.5) C = 10

8.   a.1 Mean    

9.   a.1 Mean     a.2 Median   = 103  

10. Time to travel to work (class) No. of employees (f) Class mark (x) (UC+LC)/2 fx Lower Boundary (LC-0.5) < cf (preceding frequency + succeeding frequency) 0-9 mins 14 (9+0)/2 = 4.5 63 -0.5 14 10-19 mins 26 (10+19)/2 = 14.5 377 9.5 40 20-29 mins 64 (20+29)/2 = 24.5 1568 19.5 104 30-39 mins 46 (30+39)/2 = 34.5 1587 29.5 150 40-49 mins 28 (40+49)/2 = 44.5 1246 39.5 178 50-59 mins 16 (50+59)/2 = 54.5 872 49.5 194 60-69 mins 8 (60+69)/2 = 64.5 516 59.5 202 70-79 mins 4 (70+79)/1 = 74.5 298 69.5 206

11.   a.1 Mean     a.2 Median   = 103       a.2 Mode  

12. Time to travel to work (class) No. of employees (f) Class mark (x) (UC+LC)/2 fx Lower Boundary (LC-0.5) < cf (preceding frequency + succeeding frequency) 0-9 mins 14 (9+0)/2 = 4.5 63 -0.5 14 10-19 mins 26 (10+19)/2 = 14.5 377 9.5 40 20-29 mins 64 (20+29)/2 = 24.5 1568 19.5 104 30-39 mins 46 (30+39)/2 = 34.5 1587 29.5 150 40-49 mins 28 (40+49)/2 = 44.5 1246 39.5 178 50-59 mins 16 (50+59)/2 = 54.5 872 49.5 194 60-69 mins 8 (60+69)/2 = 64.5 516 59.5 202 70-79 mins 4 (70+79)/1 = 74.5 298 69.5 206            

13.   a.1 Mean     a.2 Median   = 103       a.2 Mode      

14. Based on the grouped data below, Time to travel to work No. of employees 0-9 mins 14 10-19 mins 26 20-29 mins 64 30-39 mins 46 40-49 mins 28 50-59 mins 16 60-69 mins 8 70-79 mins 4 a. Find mean, median and mode. b. Negotiations are under consideration for payment for travelling time to work. State, giving reasons, which measure of central tendency you would use if you are (1) the employer, and (2) a trade union representing the employees.

15.   a.1 Mean     a.2 Median   = 103       a.3 Mode       b.1. As an employer = MODE = 26.2657 mins b.2. As a union representative = MEAN= 31.68 mins