Weight of the male students
Statistics
Name
Professors name
Date
Weight of the male students
Frequency distribution table
Weight in Male (lb) Frequency (f) Cumulative frequency fh H2f
110 1 3 110 12100
120 5 6 600 72000
130 3 9 390 50700
140 2 11 280 39200
150 6 17 900 135000
170 3 20 510 86700
∑h = 835 ∑f= 20 ∑fh = 2790 ∑h2f = 395700
Weight of the female students
Weight in (lb)Female Frequency (f) Cumulative frequency fh H2f
110 2 2 220 24200
120 3 5 360 43200
130 3 8 390 50700
140 5 13 700 98000
150 4 17 600 90000
170 3 20 510 86700
∑h = 835 ∑f = 20 ∑fh = 2780 ∑h2f=392800
Line graph for male and female weights (lb)
Bar graph for male and female weights (lb)
Calculation of mean, median and mode of male students (Freedman, et al, 2007)
Mean weight in male =
= = 139.5 lb
Median
Median weight of male is at = 10th and =11th position
Based on cumulative frequency 10th and 11th position are in 140
Therefore median is
= 140 lb
Modal Height
This is the weight with the highest frequency. 150 cm has the highest frequency, which is 6
Mode= 150cm
Calculation of Mean, Median and Mode of Female Students Weight (Freedman, et al, 2007)
Mean =
=
= 139 lb
Median weight for female
The median weight is at = 10th position and = 11th position
Therefore, from the cumulative frequency 10th position is at 140cm and 11th position is at 140 cm
Hence = 140cm
Modal Weight for female students
Mode is the weight with the highest frequency = 140 cm.
Standard deviation and range in male (Howell, 2011)
∑sh = ∑h2 f – = 395700-
= 395700 – 389205
=6495
Standard deviation =
= =
= 18.49
Calculating Range
Range is calculated from the table. This is the value of the highest and lowest data values, there, you identify the highest and lowest values in the value column. In the case of male, the lowest value is 110 and the highest value is 170. Then calculate their difference
The range of this data set is therefore 60
Standard deviation and range in female students
∑sh = ∑h2 f – = 392800 –
= 392800 – 386420
=6380
Standard deviation =
= =
= 18.32
Calculating range
In the case of female, the lowest value is 120 and the highest value is 170. Their difference is therefore 170-110
The range of this data set is therefore 60
Calculating a 95 per cent confidence interval for the mean of male students weight (Howell, 2011)
To calculate the confidence interval at 95% confidence level, we calculate first the sample mean
Sample mean = standard deviation divided by root of sample size
Standard deviation = 18.49
Sample size = 20
Hence, sample mean =
Sample mean is therefore, 4.13
Calculate the standard error at 95% (1.96) confidence level
Standard error = 1.96 x 4.13
= 8.10
Hence, confidence interval at 95% is calculated by adding and subtracting standard error from the mean
139.5 + 8.10 = 147.60
139.5 – 8.10 = 131.4
Comment
The two data sets have almost the same mean. Therefore, the weights of the students are not significantly different.
Calculating a 95 per cent confidence interval for the mean of female students (Freedman, et al, 2007)
To calculate the confidence interval at 95% confidence level for female, we calculate first the sample mean.
Sample mean = standard deviation divided by root of sample size
Standard deviation = 18.32
Sample size = 20
Hence, sample mean =
Sample mean is therefore, 4.472
Calculate the standard error at 95% (1.96) confidence level
Standard error = 1.96 x 4.472
= 8.765
Hence, confidence interval at 95% is calculated by adding and subtracting standard error from the mean
139 + 8.765 = 147.765
139 – 8.765 = 130.235
Calculating t-test of unpaired data using mean and standard deviation
Male students mean weight is 139.5 and standard deviation is 18.49.
Mean of female students is 139 and standard deviation is 18.32
Then compute the two to determine whether the two mean are significant from zero at 95 % level of confidence. To calculate the degree of freedom (df) is (20×2) – 2 = 40-2. Hence, degree of freedom is 38. The p value is equals 0.9320
Therefore, there is no statistically significance difference from zero
References
Freedman, D., Pisani, R., & Purves, R. (2007). Statistics (1st ed.). New York: W.W. Norton.
Howell, D. (2011). Fundamental statistics for the behavioral sciences (1st ed.). Belmont, CA: Wadsworth Cengage Learning.