displaying data- measures of dispersion

measures of dispersion definition

a measure that shows the spread of data, whether it is tightly clustered or has a broader spread

2 ways of calculating measures of dispersion

range, standard deviation

what is the range

a value that shows the spread of data, representing the difference between the lowest and highest scores

how to calculate the range

take the lowest score from the highest score and add 1

standard deviation definition

a value that represents the amount of variation of the results from the mean score

what is a small standard deviation

scores are clustered near the mean

what is a large standard deviation

scores are spread widely from the mean

what is this

the formula for standard deviation

how to calculate the standard deviation

calculate the mean for the data. subtract the mean from each score in the sample. square the result of these calculations. add the squared numbers together to find the sum of the squares. divide the sum of squares by n-1. square root

what is the x in the equation

each score in the data set

what is the x with a line above it

the mean of the data set

what is the sigma

the sum of

what is the n

number of scores in the data set

what is this an example of

table to calculate standard deviation

3 strengths of the range

easier to calculate than the standard deviation. gives an indication about the consistency/reliability of the data. appropriate for frequency data or ordinal data

2 weaknesses of the range

influenced by anomalous results- a problem because only the highest and lowest scores are considered in the calculation. doesnt consider distribution of scores around the mean, therefore we are unsure if the results are similar or spread out

4 strengths of standard deviation

more sophisticated/representative measure of dispersion than range- reflects every score in data set. gives indication of how close scores are to the mean (in a normal distribution). less sensitive to anomalies than range. appropriate for interval or ratio data

2 weaknesses of standard deviation

more time consuming to calculate compared to the range. not all scores will be within one standard deviation so it can be misleading when it comes to anomalies

what is a normal distribution

a type of distribution where the mean, median and mode are equal. can be referred to as a bell curve

examples of normal distributions in real life

height, weight, shoe size

5 features of a normal distribution

bell shaped. has mean, median and mode together at midpoint. symmetrical at midpoint. 50% of scores are to the left and 50% to the right. curve end points meet at y axis

what is this an example of

normal distribution curve

what is a positive skewed distribution

the most common score (mode) is lower than the median, and is also lower than the mean. bunched to the left and tail to thr right.

in cases of positively skewed distribution, what happens to the central tendency? (mean,median and mode)

decrease in value

what is a negative skewed distribution?

the most common score (mode) is greater than the median, and is also greater than the mean. bunched to the right and tail to the left

is this positive or negatively skewed

positive skewed

is this positively or negatively skewed

negative skewed

what isthis

standard deviation curve

what percent of data falls within ONE standard deviation, either side of the mean?

68%

what percent of data falls within TWO standard deviations, either side of the mean?

95%

what percent of data falls within THREE standard deviations, either side of the mean?

99.7%

what numbers are probabilities written from and to

0-1

what is a probability value and what is it usually?

a numerical value that gives an indication of the likelihood that results are due to a real difference/correlation and not due to chance. usually 95%

what is a significance level and what is it usually?

a numerical value that is usually expressed to two decimal places. tells you the margin of error than could occur in your results. usually 0.05

what does a significance level of 0.05 tell you

there is a 5% probability that the results are due to chance and not the correlation between variables

what is a strict significance level

0.01

what is a lenient significance level

1