Question

The following data represent baseball batting averages for a random sample of National League players near the end of the baseball season. The data are from the baseball statistics section of The Denver Post.

0.194 0.258 0.190 0.291 0.158 0.295 0.261 0.250 0.181 0.125 0.107 0.260 0.309 0.309 0.276 0.287 0.317 0.252 0.215 0.250 0.246 0.260 0.265 0.182 0.113 0.200

(a) Multiply each data value by 1000 to "clear" the decimals. (Keep data values in the same order they appear in the table above.)

(b) Use the standard procedures of this section to make a frequency table with your whole-number data. Use five classes.

(c) Divide class limits, class boundaries, and class midpoints by 1000 to get back to your original data values.

Answer 1

According to the given data :

0.194	0.258	0.190	0.291	0.158	0.295	0.261	0.250	0.181	0.125	0.107	0.260	0.309
0.309	0.276	0.287	0.317	0.252	0.215	0.250	0.246	0.26	0.265	0.182	0.113	0.200

a) After multiplied by 1000 we get :

194	258	190	291	158	295	261	250	181	125	107 (L)	260	309
309	276	287	317 (H)	252	215	250	246	260	265	182	113	200

b) in order to construct a frequency table by using a the standard procedures, we follow the following steps:

Step-I:

The highest and lowest observation are 317 and lowest 107 ,therefore the range is :

As we need five equal classes, therefore he class width is determined as:

Class width= ( range/required classes)

Therefore frequency table with 5 classes and class width is 42.

Therefore the frequency table is:

Class boundary can be constructed by lower of 0.5 from lower class interval and adding 0.5 to the upper class interval in corresponding class interval to the calss boundaries.

We consider 0.5 as the difference between two consecutive class interval is 1 and therefore we add to get upper bounadry and deduct 0.5 to get lower boundary.

We assing tally marks for measuring frequency to the corresponding class interval.

Mid point is determined as:

Mid point=( Lower class interval limit +Upper class interval limit)/2

Class Interval	Class Boundary	Tally marks	Frequency	Mid Point
107-149	106.5-149.5	III	3	128
150-192	149.5-192.5	IIII	4	171
193-235	192.5-235.5	III	3	214
236-278	235.5-278.5	IIIII IIIII	10	254
279-321	278.5-321.5	IIIII I	6	300

c) Divide class limits, class boundaries, and class midpoints by 1000 to get back to your original data values:

Class Interval	Class Boundary	Tally marks	Frequency	Mid Point
0.107-0.149	0.1065-0.1495	III	3	0.128
0.150-0.192	0.1495-0.1925	IIII	4	0.171
0.193-0.235	0.1925-0.2355	III	3	0.214
0.236-0.278	0.2355-0.2785	IIIII IIIII	10	0.254
0.279-0.321	0.2785-0.3215	IIIII I	6	0.300