Download presentation

Published byJulia Shaddix Modified over 2 years ago

1
3.3 Measures of Position Measures of location in comparison to the mean. - standard scores - percentiles - deciles - quartiles

2
**Z score or Standard Score**

90 on a music test vs 45 on an English test The Z score tells us how many standard deviations a data value is above or below the mean.

3
**Z score or Standard Score**

The Z score tells us how many standard deviations a data value is above or below the mean. -Subtract the mean from the value and divide by standard deviation Z = population sample Z=

4
A student scores a 65 on a calc test that has a mean of 50 and a standard deviation of 10. She scored a 30 on a history test with a mean of 25 and standard deviation of 5. Compare her relative positions on the two tests.

5
Test 1: X = 38, X = 40 and s = 5 Test 2: X = 94, X = 100, s = 10

6
**A set of data has a mean of 105 and a standard deviation of 8**

A set of data has a mean of 105 and a standard deviation of 8. Find the data values that correspond to the following z scores. a. 2 b. -1 c. 0 d. -1.6

7
Percentiles Percentiles divide the data set into 100 equal groups

9
**Percentiles are symbolized by P1,P2, P3, ...P100**

Dividing the distribution into 100 groups. P99 P1 P2 1% 1% 1%

10
Percentiles The percentile corresponding to a given value X is found using the following formula: (number of values below X) + .5 100% Percentile = total number of values

11
**A teacher gives a 20 point test to 10 students**

A teacher gives a 20 point test to 10 students. Find the percentile rank of the score of 12. Then find the percentile rank of the score of 6. 18,15,12,6,8,2,3,5,20,10

12
18,15,12,6,8,2,3,5,20,10 Now use the data to determine the value corresponding with the 25th percentile. n = # values p = percentile Formula to use: c = n*p 100 if c is not a whole number: round up to the nearest whole number if c is a whole number find the value halfway between the cth term and the c+1 term

13
**Find the value that corresponds to the 60th percentile**

2,3,5,6,8,10,12,15,18,20

14
The frequency distribution for the systolic blood pressure readings (in mm or mercury) of 200 randomly selected college students is shown here. Construct a Percentile Graph. Boundaries Frequency cumulative frequency cumulative percent 24 62 72 26 12 4

15
**Cumulative Percentages**

Class Boundaries

16
Quartiles Quartiles divide the distribution into 4 groups: Q1,Q2,Q3, Q1 --> is the same as P25 or 25th percentile Q2 --> is the same as P50 or 50th percentile Q3 --> is the same as P75 or 75th percentile

17
MD largest data value smallest data value Q1 Q2 Q3 25% 25% 25% 25%

18
Finding the Quartiles Q2 --> The Median! Q1 --> The median of the data below Q2 Q3 --> The median of the data above Q2

19
**Find Q1,Q2 and Q3 for the following data set.**

15,13,6,5,12,50,22,18

20
**Deciles Deciles divide the data into ______ groups.**

We can use the formula for Percentiles to find Deciles

21
Interquartile Range Quartiles can be used as a rough measurement of variability Interquartile Range: (IQR) the difference between Q3 and Q1. Or the range of the middle 50% of the data. We can use the IQR to identify outliers

22
Outlier An extremely high or extremely low value when compared to the rest of the data. Outliers affect: - mean -standard deviation -range

23
**How do we determine if a value is high or low enough to be an outlier?**

1. Put the data in order and find the quartiles. 2. Find IQR 3. Multiply the IQR by 1.5 4. Subtract the product from Q1 and add it to Q3. 5. If there are any values lower or higher than those two values, they are considered outliers.

24
**Check the following for outliers**

5,6,12,13,15,18,22

25
**Using the Calculator 1. Enter data into L1 2. Press stat**

3. Move the arrow 1 right to Calc 4. Press 1 for Var-Stats 5. Press 2nd L1 then enter

26
**Using the Calculator Your calculator will display the following:**

x: sample mean x: sum of the data values x2: sum of the squares of the data values Sx: sample standard deviation : population standard deviation minX: smallest data value Q1: lower quartile Med: median Q3: upper quartile maxX: largest data value

27
Using the Calculator Use your calculator to find the stats on the following data: 11.2, 11.9, 12.0, 12.8, 13.4, 14.3

28
**Using the Calculator For grouped data... 1. Enter midpoints into L1**

2. Enter frequencies into L2 3. Press stat button 4. Use arrow to move 1 right to calc 5. Press 1 for vars stats 6. Press 2nd L1 and 2nd L2 then enter

29
Using the Calculator Find the mean and standard deviation of the following data. 1 8 2 13 3 18 5 23 4 28 33 38

30
Using the Calculator Graph a percentile graph on your calculator 1 2 3 5 4

Similar presentations

OK

Chapter 3.3 Measures of Position. Standard Score A comparison that uses the mean and standard deviation is called a standard score or a z-score A.

Chapter 3.3 Measures of Position. Standard Score A comparison that uses the mean and standard deviation is called a standard score or a z-score A.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on our environment for class 5 Ppt on measures of central tendency Ppt on text to speech converter free download Ppt on revolt of 1857 leaders Ppt on as 14 amalgamation process Ppt on sea level rise news Ppt on supply chain management of hyundai motors Ppt on fire extinguisher training Team based pay ppt online Ppt on total hip replacement