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Statistics has three meanings:
Expt | Run | Speed | |
---|---|---|---|
001 | 1 | 1 | 850 |
002 | 1 | 2 | 740 |
003 | 1 | 3 | 900 |
004 | 1 | 4 | 1070 |
005 | 1 | 5 | 930 |
006 | 1 | 6 | 850 |
40, 39, 31, 38, 40, 40, 34, 39, 31, 38, 37, 30, 31, 37, 35, 37, 36, 35, 39, 39
x | Freq |
---|---|
30 | 1 |
31 | 3 |
34 | 1 |
35 | 2 |
36 | 1 |
37 | 3 |
38 | 2 |
39 | 4 |
40 | 3 |
X = 11, 15, 16, 18, 20, 22, 25
Class | Tally | Frequency |
---|---|---|
11-15 | || | 2 |
16-20 | ||| | 3 |
21-25 | || | 2 |
Range = (Highest value - Lowest value) + 1
X = 11, 15, 16, 18, 20, 22, 25
Range of X = ?
Class Interval
\((11-15) \rightarrow (15-11+1)= 5\), not 4
X = 32, 20, 34, 17, 15, 40, 5, 18, 44, 28, 49, 27, 8, 29, 45, 39, 3, 35, 46, 37, 50, 36, 2, 4, 7, 24, 42, 31, 19, 14
Range = ?
Let, class interval = 5
Number of class = ?
Class (Marks out of 40) | Frequency |
---|---|
11-15 | 2 |
16-20 | 5 |
21-25 | 9 |
26-30 | 10 |
31-35 | 3 |
Class (Marks out of 40) | Frequency | Cumulative Frequency |
---|---|---|
11-15 | 2 | 2 |
16-20 | 5 | 7 |
21-25 | 9 | 16 |
26-30 | 10 | 26 |
31-35 | 3 | 29 |
Make sure class intervals are continuous
Continuous or exclusive: (10-15); (15-20); (20-25) Discontinuous/Inclusive: (10-14); (15-19)
Conversion
Continuous CI | Discontinuous CI |
---|---|
10-14 | 9.5-14.5 |
15-19 | 14.5-19.5 |
20-24 | 19.5-24.5 |
25-29 | 24.5-29.5 |
Interval | Frequency |
---|---|
20-30 | 5 |
30-40 | 12 |
40-50 | 30 |
50-60 | 40 |
60-70 | 20 |
70-80 | 13 |
80-90 | 3 |
90-100 | 2 |
Write its interpretation in 3-5 sentences.
Class Interval | Continuous CI | Frequency |
---|---|---|
11-20 | 10 | |
21-30 | 20 | |
31-40 | 35 | |
41-50 | 20 | |
51-60 | 15 | |
61-70 | 10 | |
71-80 | 8 | |
81-90 | 5 | |
91-100 | 3 |
Histogram
Somoothed version of frequency polygon
intervals | CF |
---|---|
0-5 | 1 |
5-10 | 2 |
10-15 | 4 |
15-20 | 6 |
20-25 | 7 |
25-30 | 10 |
\[AM = \frac 1 n \sum_{i=n}^n f_ix_i \]
Calculate the mean in a smart way
## [1] 1009 1037 1047 1024 1013 1043
Subtract a number from all, say 1020
## [1] "The new values are"
## [1] -11 17 27 4 -7 23
## [1] "Mean of y is 8.83"
## [1] "Mean of x is 1028.83"
Consider the values: 1005, 1010, 1015
If 1000 is subtracted: 5, 10, 15
If again divided by 5: 1, 2, 3
Converted Mean = 2
Original Mean = \(2 \times 5 + 1000=1010\)
x = 1005, 1010, 1015