Question

1. Which of the following is true about the median?
   1. The median and the 50^th percentile are the same
   2. The median is more sensitive to outliers than the mean
   3. The median and the 2^nd quartile are the same
   4. Both A and C are correct

Use the following data for problems 2-4.

Crusty’s Pizza sampled 10 new stores that had the following sales last week (note, data is a sample).

Store	Sales	Most popular pizza
A	12310	Cheese
B	15742	Pepperoni
C	9685	Hawaiian
D	7852	Pepperoni
E	10254	Vegetarian
F	8812	Vegetarian
G	3421	Pepperoni
H	6842	Hawaiian
I	4298	Pepperoni
J	9908	Pepperoni

2. What is the average Sales?
   1. 7845.1
   2. 10912.6
   3. 8912.4
   4. 11094.2

3. What is the standard deviation?
   1. 13202258.9
   2. 3627.74
   3. 3426.69
   4. 1425.64

4. What is the mode for the “most popular pizza” variable?
   1. 5
   2. Pepperoni
   3. Cheese
   4. Qualitative variables do not have a mode

Answer 1

Sales Workings Most Popular Store Pizza Cheese Pepperoni Hawaiian Pepperoni Vegetarian Vegetarian Pepperoni Hawaiian Pepperoni Pepperoni Total - - IOT MOOD d = Sales - x 12,310 3,397.60 15,742 6,829.60 9,685 772.60 7,852 -1,060.40 10,254 1,341.60 8,812 -100.40 3,421 -5,491.40 6,842 -2,070.40 4,298 -4,614.40 9,908 995.60 89,124 d^2 1,15,43,685.76 4,66,43,436.16 5,96,910.76 11,24,448.16 17,99,890.56 10,080.16 3,01,55,473.96 42,86,556.16 2,12,92,687.36 9 ,91,219.36 11,84,44,388.40 $ Average (x) = | Total Sales / no of stores $89124 / 10 8,912.40 Satndard Deviation = Sum of d^2 Jn-1 118448388.40 10 – 1 3627.74

Solution 1. Option D -Both the options A and C are correct Median is the mid Value, therefore 50th percentile which is the mid value and 2nd Qaurtile which is also the mid value, all the same Solution 2. The Average sales is calculated in the above working Option C - $8,912.40 is the correct answer Solution 3. Standard deviation is calculated in the above workings Option B - $3627.74 is the correct answer Solution 4. Mode is the highest frequency In the above table, "Most popular Pizza" has Pepperoni which is having the highest frequency 5 times Thus, Option A-5 is the correct answer

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