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# Statistics

(i) A production manager at a firm recorded the outputs of the all workers in the production division during a certain shift and obtained the following results.
1496 1377 1336 1103 1284 1459 1401 1535
1519 1390 1355 1228 1329 1484 1440 1674
1505 1385 1339 1162 1310 1462 1401 1568
1517 1388 1347 1227 1322 1483 1406 1605
1526 1392 1362 1232 1335 1491 1443 1693
1.1 Use the stem and leaf method to construct a grouped frequency distribution of the above data.
Use a total of six classes and let 1100 units be the lower limit of the smallest class. (5)

Solution:
Frequency Stem Leaf
2 11| 03 62
4 12 | 27 28 32 84
14 13| 10 22 29 35 36 39 47 55 62 77 85 88 90 92
11 14| 01 01 06 40 43 59 62 83 84 91 96
6 15| 05 17 19 26 35 68
3 16 | 05 74 93
Key: 16|05 means 1605.
Frequency distribution is shown below in the table
Class Frequency
1100-1199 2
1200-1299 4
1300-1399 14
1400-1499 11
1500-1599 6
1600-1699 3

1.2 Use the grouped data of 1.1 to determine the mean, median and modal outputs. Interpret you results.
1.3 Draw to scale the cumulative frequency polygon for the above data.
1.4 Use the cumulative frequency polygon to estimate the interquartile range. Interpret the result you obtained.
1.5 Calculate the 70th percentile using:
1.5.1 the raw data given in the table above.
1.5.2 the grouped frequency distribution.
1.5.3 the less than cumulative polygon.

#### Solution Summary

A Complete, Neat and Step-by-step Solution is provided in the attached Excel file.

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