measures of central tendency (contd…) prepared by: bhakti joshi date: november 28, 2011
TRANSCRIPT
Measures of Central Tendency (Contd…)
Prepared by: Bhakti JoshiDate: November 28, 2011
Frequency distribution of Weights in Pounds of a sample of packages
Weights Class Frequency of packages (f) Mid-point (x) fx
10.0 – 10.9 1 (10+10.9)/2= 10.5 1*10.5= 10.5
11.0 – 11.9 4 11.5 4*11.5= 46
12.0 – 12.9 6 12.5 6*12.5=75
13.0 – 13.9 8 13.5 8*13.5= 108
14.0 – 14.9 12 14.5 12*14.5= 174
15.0 – 15.9 11 15.5 11*15.5=170.5
16.0 – 16.9 8 16.5 8*16.5=132
17.0 – 17.9 7 17.5 7*17.5=122.5
18.0 – 18.9 6 18.5 6*18.5=111
19.0 – 19.9 2 19.5 2*19.5=39
65 988.5
15.2
Monthly Average Cash Balances of 600 customers
Class (Rupees) Frequency of Customers (f) Mid-point (x) fx
0 – 49.9 78 (0+49.9)/2= 25 78*25= 1950
50.00 - 99.99 123 75 9225
100.00 - 149.99 187 125 23375
150.00 - 199.99 82 175 14350
200.00 – 249.99 51 225 11475
250.00 – 299.99 47 275 12925
300.00 - 349.99 13 325 4225
350.00 – 399.99 9 375 3375
400.00 – 449.99 6 425 2550
450.00 – 499.99 4 475 1900
600 85,350
142.25
Median
Roll No. Age
1 182 183 184 185 196 167 188 179 1810 18
…Central Item of a data set
(N+1) /2 = MN = Number of observationsM= Median
Median
Age Intervals
Frequency of Mobile
Phones Owned (f)
Cumulative Frequency
10 - 15 20 20
15 - 20 40 60
20 - 25 60 120
25 - 30 70 190
30 - 35 60 250
35 - 40 30 280
40 - 45 20 300
Interpretation?
Estimated median weight of the fish caught
Weights Intervals
Frequency of fish
caught (f)
Cumulative Frequency
10-19.5 8 820-29.5 15 2330-39.5 23 4640-49.5 37 8350-59.5 46 12960-69.5 52 18170-79.5 84 26580-89.5 97 36290-99.5 16 378100-109.5 5 383
Item or number that represents median
383+1 / 2= 192nd item
Class that contains the median item
70 – 79.5
Width of the weights interval9.5
Estimated median value?(192 – (181+1) 84
* 9.5 + 70 =
71.13
Mode…Value that is repeated most often in the data set. Mode is not used for ungrouped data
Age Intervals
Frequency of Mobile
Phones Owned (f)
Cumulative Frequency
10 - 15 20 20
15 - 20 40 60
20 - 25 60 120
25 - 30 70 190
30 - 35 60 250
35 - 40 30 280
40 - 45 20 300
Interpretation?
Relationship between Mean-Median-Mode
• Mean < Median < Mode = Negatively (left) Skewed
• Mean> Median> Mode = Positively (right) Skewed
• Mean = Median = Mode = Normal
Negatively (left) Skewed
Positively (right) Skewed
Normal
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Frequency and Distribution Curve
Geometric Mean