MTH-101 Module 8: Sampling and Descriptive Statistics

MTH 101Descriptive Statistics
Define the following terms and describe how to find the appropriate value, if necessary.
1.) Mean :
2.) Median: split the data set in half.
3.) Deviation:
4.) Variance :The average (using N-1 instead of that number of value ) of the square of the
deviations.
𝑆2 =
∑(𝑥−𝑋)^2
𝑛−1
5.) Standard Deviation: the square root of the variance. It shows the spread of data. The larger the
standard deviation, the more widespread the data. The smaller the standard deviation the
standard deviation, the closer the data lie to the mean
𝑆=√
∑(𝑥 − 𝑥)^2
𝑁−1
Use your knowledge of the terminology to answer the following questions. If needed, round answers
to two decimal places.
1.) What is another word to describe the ‘mean’?
Average
2.) Given the following data set, find the mean and median.
4, 5, 7, 9, 11, 12, 14, 16, 18
Mean≈ 10.67
Median≈ 11
MTH 101
3.) Given the following data set, find the mean and median.
5, 6, 7, 7, 7, 8, 9, 10
4.) Estimate the mean and median from the frequency table given below.
Value
Frequency
12
9
13
6
14
4
15
7
16
4
5.) Estimate the mean from the frequency table below. Notice, these values are given in intervals.
Remember to start by finding the midpoints! Add to values and divide by 2
Value Interval
Frequency
7-9
9
10 – 12
6
13 – 15
7
16 – 18
3
19 – 21
5
Mean=72+66+98+51+100/30=12.9
Median= 11+14/2=25/2+12.5
MTH 101
6.) To find the standard deviation, we start by finding the _Mean_____ of the data set. Then, we take
each data value and __Substract___ the mean. We will _square____ each of these numbers before
taking the
sum. Once we have added these values, we will _divide____ by n – 1. Now we have found variance.
So to find the standard deviation, our last step is to take the ___Square root__ _____ of the variance.
7.) If the given sample variance is 17.56, what is the standard deviation?
√17.5 = 4.18
8.) Find the sample variance and standard deviation of the following set of numbers. The table has been
given to you to help with organization.
6, 8, 11, 14, 18
Value
6
Value – Mean
-5.4
(Value – Mean)^2
29.16
8
-3.4
11.56
11
-0.4
0.56
14
2.6
6.76
18
6.6
43.56
9.) Find the sample variance and standard deviation of the following set of numbers. The table has
been given to you to help with organization.
MTH 101
21, 24, 24, 27, 29, 33, 37
Value
21
24
24
27
29
33
37
Value – Mean
(Value – Mean)^2
MTH 101
How Old Do You Feel?
Each person in the class shall come to the front of the class and write how old they feel on the front
board. You will use this collection of data to answer the following questions.
1.) Create a frequency table using the data from the class and include the relative frequency. Round
to two decimal places if necessary. You may use intervals if necessary. Discuss with your partner!
(Add more rows as necessary.)
Data Value (or Interval)
Frequency
Relative Frequency
2.) Create a frequency histogram using your table from #1.
3.) Find the mean, median, variance and standard deviation for the original data set. Do not use intervals
from your table! Round to two decimal places as needed.
Mean =
Median =
Variance =
Standard Deviation =
4.) Based on the standard deviation found above, what inference can you make about your data?
MTH 101