Question

In a survey, people were asked to "randomly pick a whole number between 1 and 20" Here are the responses
3   3   3   4   4   5   7   7   7   8   11   12  
13   13   13   13   13   15   15   16   17   17   17   17
17   17   17   18   19   29
Compute the
mean
median
mode
standard deviation
Q1
Q3
IQR
Based on the mean and median describe the shape of the data:

create a graph of the data and describe the shape of data in a sentence

Answer 1

Solution:

n = Number of Data Values = 30

Sum of Data Values = Σxᵢ = 370

Sample Mean = x̄ = Σxᵢ / n = 370 / 30 = 12.33

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

3   3   3   4   4   5   7   7   7   8   11   12   13   13   13   13   13   15   15   16   17   17   17   17   17   17   17   18   19   29   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median= 13 +13 / 2 = 13

The mode of a set of data is the value in the set that occurs most often.

Ordering the data from least to greatest, we get:

3   3   3   4   4   5   7   7   7   8   11   12   13   13   13   13   13   15   15   16   17   17   17   17   17   17   17   18   19   29   

We see that the mode is 17 .

s = Sample Standard Deviation = √ Sample Variance = √37.81609195402311 = 6.14

Q1 = First Quartile = Middle of First Half of Data Set = 7

Q3 = Third Quartile = Middle of Second Half of Data Set = 17

IQR = Interquartile Range = Q3 - Q1 = (17) - (7) = 10

Four sub parts per answer