Question

Main idea: You are given 30 pieces of data. You will then use the data to make a grouped frequency distribution, a frequency histogram, and frequency polygon, find the mean, median, mode, range, and standard deviation. Round to the nearest tenth when necessary.

79 51 67 50 78 62 89 83 73 80 88 48 60 71 79 89 63 55 93 71 41 81 46 50 61 59 50 90 75 61 1.

Using the data, find the mean, median, mode, range, and standard deviation.

2. Using all of your original data, construct a grouped frequency distribution. The grouped frequency distribution needs at least 4 intervals and each interval must have the same range and no overlap. Begin with the interval 40-49.

3. Using the grouped frequency distribution, draw a histogram.

4. Draw a Normal Distribution Curve. Label all components appropriately. Make sure to include up to plus three and minus three standard deviation labels on your curve.

5. Answer. What percentage of the sample population falls above – 1 standard deviation. Show all of your work on how you came to your answer. Then come up with one additional question and show your solution in detail. This should be solved and shown as if you were going to present your conclusions at a business meeting.

Answer 1

Although the question is from Statistics, I will provide the solution to it.

1. Mean = Sum of All 30 numbers / 30 = 2043 / 30 = 68.1

Median = Sum of 15th Number and 16th Number (In ascending or descending order) / 2 = (67 + 71)/2 = 69

Mode = The number which apprears the maximum times among the set of 30 numbers = 50

Range = Higher number - Lowest number = 93- 41 = 52

Standard deviation = 14.953

2. Frequency distribution table:

Class Interval	Frequency
40 - 49	3
50 - 59	6
60 - 69	6
70 - 79	7
80 - 89	6
90 - 99	2

3. Histogram of grouped frequency distribution:

4. Normal Distribution curve is mentioned herewith.

Mean - 3*SD	23
Mean - 2*SD	38
Mean - 1*SD	53
Mean	68
Mean + 1*SD	83
Mean + 2*SD	98
Mean + 3*SD	113

Class interval	Frequency distribution
23 - 38	0
38 - 53	7
53 - 68.1	8
68.1 - 83	10
83 - 98	5
98 - 113	0

5. Percentage of population above -1 standard deviation = (8+10+5)/30 = 23 / 30 = 76.67 %

Thus, you can figure out from the distribution that maximum concentration is around the Mean + 1 standard deviation. It means that it is perfectly following the normal distribution curve.

Hope this clarifies the query.