The intelligence quotients (IQs) of 16 students from one area of a city showed a mean of 107 and a standard deviation of 10, while the IQs of 14 students from another area of the city showed a mean of 112 and a standard deviation of 8. Use alpha = 0.01. What is the pooled standard deviation?

Lexi Mcneil 2022-07-16 Answered
The intelligence quotients (IQs) of 16 students from one area of a city showed a mean of 107 and a standard deviation of 10, while the IQs of 14 students from another area of the city showed a mean of 112 and a standard deviation of 8. Use alpha = 0.01. What is the pooled standard deviation?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (2)

wintern90
Answered 2022-07-17 Author has 12 answers
n 1 = 16
n 2 = 14
x 1 ¯ = 107
x 2 ¯ = 112
s 1 = 10
s 2 = 8
Pooled standard deviation is defined as an estimate of standard deviation when different groups are assumed to have the same standard deviation.
The pooled variance is given by:
S p 2 = ( n 1 1 ) s 1 2 + ( n 2 1 ) s 2 2 n 1 + n 2 2 = ( 16 1 ) 10 2 + ( 14 1 ) 8 2 16 + 14 2 = 2332 28 = 83.2857
The pooled sd is given by:
s d = 83.2857 = 9.1261
Did you like this example?
Subscribe for all access
Darian Hubbard
Answered 2022-07-18 Author has 7 answers

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-11-18
What is the mathematical formula for the pooled variance of two populations?
asked 2022-08-12
What is pooled standard deviation and how is it calculated ?
asked 2022-09-30
How do you find the pooled standard deviation in an ANOVA table?
asked 2022-07-22
Comparison between two diets in obese children, one low-fat and one low-carb 8 week intervention with the outcome of weight loss. Based on a similar study in adults, 20% of the children will not complete the study. For a 95% confidence interval with a margin of error of no more than 3 lbs., how many children should be recruited? In the adult trial, the low-fat and low-carb groups had a standard deviations of 8.4 and 7.7, respectively and each group had 100 participants.
A. Calculate the pooled standard deviation (Sp).
B. Calculate the number of children will need to be recruited for the trial if all finish the study use the Sp calculated for the standard deviation?
C. How many children would be needed to account for 20% attrition.
asked 2022-09-28
The denominator of the t score formula for the independent-samples t-test is ______.

1 - population standard error
2 - estimated pooled standard deviation
3 - estimated pooled variance
4 - estimated standard error
asked 2022-07-01
I have 2 groups of people. I'm working with the data about their age. I know the means, the standard deviations and the number of people. I don't know the data of each person in the groups.
Group 1 :
Mean = 35 years old; SD = 14; n = 137 people
Group 2 :
Mean = 31 years old; SD = 11; n = 112 people
I want to combine those 2 groups to obtain a new mean and SD. It's easy for the mean, but is it possible for the SD? I do not know the distribution of those samples, and I can't assume those are normal distributions. Is there a formula for distributions that aren't necessarily normal?
asked 2022-09-27
Find the pooled estimate of the standard deviation if n1 = 18, n2 = 14, S1= 3.3, and S2= 2.5.
(Write two decimal places)

New questions