14. Considering the following distribution Calculate: A) median B) All quartiles. C) The 5^ (th ) and 8^ (th ) decile. D) The 50^ (th ) and 80^ (th ) percentile. Values & Frequency 140-150 & 17 150-160 & 29 160-170 & 42 170-180 & 72 180-190 & 84 190-200 & 107 5 Do with a group of 5 members! 200-210 & 49 210-220 & 34 220-230 & 31 230-240 & 16 240-250 & 12

## Step 1: Calculate the Total Frequency### Sum all the frequencies to find the total number of observations. The frequencies are: 17, 29, 42, 72, 84, 107, 49, 34, 31, 16, and 12. Adding these gives a total frequency . ## Step 2: Calculate the Median### The median is the value that divides the dataset into two equal halves. For grouped data, the median can be found using the formula: Where:- is the lower boundary of the median class.- is the cumulative frequency before the median class.- is the frequency of the median class.- is the class width.### Find the Median Class- - Locate the class where the cumulative frequency exceeds 246.5. This occurs in the class 190-200.### Calculate the Median- , (cumulative frequency up to 180-190), , ## Step 3: Calculate Quartiles### First Quartile ( )- position is at - Locate the class where the cumulative frequency exceeds 123.25. This occurs in the class 170-180. ### Third Quartile ( )- position is at - Locate the class where the cumulative frequency exceeds 369.75. This occurs in the class 200-210. ## Step 4: Calculate Deciles### Fifth Decile ( ) is the same as the median, so .### Eighth Decile ( )- position is at - Locate the class where the cumulative frequency exceeds 394.4. This occurs in the class 200-210. ## Step 5: Calculate Percentiles### Fiftieth Percentile ( ) is the same as the median, so .### Eightieth Percentile ( )- position is at - This is the same calculation as for , so .