maths skills

Question 1

what does standard deviation do?

Answer 1

shows by how much the members of a group differ from the mean value for the group (variability or spread about the mean)

Question 2

what does a high standard deviation mean?

Answer 2

there is a high variability of data, so the mean is less reliable

Question 3

how can the reliability of the mean be improved?

Answer 3

by using a larger sample size

Question 4

how do you calculate standard deviation?

Answer 4

√∑(xi - x‾)^2/ n-1

Question 5

what does each symbol mean?

Answer 5

xi = individual number
x‾ = mean
∑ = sum of
n = sample size (number of values)
essentially the square root of each individual number - the mean and then squared, and then add this together for each value and divide by the sample size - 1

Question 6

how do you find the mean/standard deviation on a calculator?

Answer 6

1. switch to the statistics function
2. select 1-variable
3. input each number from the data set and press equals after each one
4. once all numbers are inputted, press equals again
5. select 1-Var results
6. the value next to x‾ tells you the mean
7. the value next to sx tells you the standard deviation (scroll down)

Question 7

what is the variance of a set of values?

Answer 7

the standard deviation squared

Question 8

when do you carry out a t test?

Answer 8

if you want to find out whether there is a significant difference between two means

Question 9

what are the steps to carrying out a t test?

Answer 9

1. state the null hypothesis
2. calculate the value of t
3. calculate the degrees of freedom (n-1)
4. compare t to the critical value in the probability table
5. write a conclusion

Question 10

what is a null hypothesis (Ho)?

Answer 10

a negative statement which you are looking to disprove ie. there is no significant difference between two means

Question 11

conclusion - what do you do if the value of t is equal to or greater than the critical value at the 0.05 probability?

Answer 11

reject the null hypothesis
there is less than 0.05 probability that the difference between the means occurred by chance
there is a significant difference between the means

Question 12

conclusion - what do you do if the value of t is less than the critical value at the 0.05 probability?

Answer 12

accept the null hypothesis
there is greater than 0.05 probability that the difference between the means occurred by chance
there is no significant difference between the means