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Measures of relative standing - z-score, quartiles, percentiles
- Intro Lesson: a10:21
- Intro Lesson: b3:45
- Intro Lesson: c1:15
- Intro Lesson: d5:44
- Lesson: 15:07
- Lesson: 2a4:25
- Lesson: 2b5:33
- Lesson: 2c3:32
- Lesson: 3a4:16
- Lesson: 3b0:59
- Lesson: 3c2:56
- Lesson: 3d4:11
- Lesson: 4a3:39
- Lesson: 4b2:18
Measures of relative standing - z-score, quartiles, percentiles
Lessons
⋅ zx: z-score, a measure of how many standard deviations a data item x is from the mean.
population: zx=σx−μ
sample: zx=sx−x
z-score allows comparison of the variation in different populations/samples.
⋅ Quartiles: values that divide the data set into quarters.
Q1= bottom 25% of data
Q2= Median = bottom 50% of data
Q3= bottom 75% of data
⋅ InterQuartile Range (IQR): represents the middle 50% of the data set.
IQR=Q3−Q1
⋅ Percentiles: indicates what percentage of the data falls below a certain value
PercentileofX=totalnumberofdatapointsnumberofdatapointslessthanX
⋅ Outliers: an outlier is a data point which lies an abnormal distance from all other data points.
Outliers are either,
a) above Q3+1.5(IQR) or b) below Q1−1.5(IQR)
population: zx=σx−μ
sample: zx=sx−x
z-score allows comparison of the variation in different populations/samples.
⋅ Quartiles: values that divide the data set into quarters.
Q1= bottom 25% of data
Q2= Median = bottom 50% of data
Q3= bottom 75% of data
⋅ InterQuartile Range (IQR): represents the middle 50% of the data set.
IQR=Q3−Q1
⋅ Percentiles: indicates what percentage of the data falls below a certain value
PercentileofX=totalnumberofdatapointsnumberofdatapointslessthanX
⋅ Outliers: an outlier is a data point which lies an abnormal distance from all other data points.
Outliers are either,
a) above Q3+1.5(IQR) or b) below Q1−1.5(IQR)
- Introductiona)Z-Scoreb)Quartilesc)InterQuartile Ranged)Percentiles
- 1.Using Z-score to Compare the Variation in Different Populations
Charlie got a mark of 85 on a math test which had a mean of 75 and a standard deviation of 5. Daisy got a mark of 75 on an English test which had a mean of 69 and a standard deviation of 2. Relative to their respective mean and standard deviation, who got the better grade? - 2.Determining the Quartiles
Find the quartiles for each data set:a){9, 3, 7, 5, 2, 8, 12}b){2, 3, 5, 7, 8, 9, 12, 15}c){2, 3, 5, 7, 8, 9, 12, 15, 35} - 3.Interquartile Range & Box-and-Whisker Plot
For the data set: {8, 2, 20, 4, 9, 5, 6, 12, 10, 1}a)Determine the quartiles.b)Find the interquartile range.c)Construct a box-and-whisker plot.d)Which data points, if any, are outliers? - 4.Determining the Percentile
Sidney is taking a biology course in university. She got a mark of 78% and the list of all marks from her class (including her mark) is given by {56, 83, 74, 67, 47, 54, 82, 78, 86, 90}.a)What percentile did she score in?b)Sidney's friend Billy knows he got in the 70% percentile, what was his mark?