Question 18 The weight of coffee in 70 packets are shown in the following table beginarray 1 - hline Weightin g - Number of packetslllhline 200-201812 1201-202826 1202-203820 1203-204-911204-205-2W205-20681111hlineend array Determine the model weight-

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Standard X

Mathematics

Mode for Grouped Data

Question 18 T...

Question

Question 18
The weight of coffee in 70 packets are shown in the following table
Weight
200-201
201-202
202-203 203-204 204-205 205-206
Number of packets
12 26 20 9 2 1

Determine the model weight.

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Solution

In the given data, the highest frequency is 26, which lies in the interval 201-202
Here, $l = 201$
$f_{m} = 26, f_{1} = 12, f_{2} = 20$ and (class width) h = 1
$∴$ Mode $= l + (\frac{f_{m} - f_{1}}{2 f_{m} - f_{1} - f_{2}}) \times h \Rightarrow Mode = 201 + (\frac{26 - 12}{2 \times 26 - 12 - 20}) \times 1$
$= 201 + (\frac{14}{52 - 32}) = 201 + \frac{14}{20} = 201 + 0.7 = 201.7 g$
Hence, the modal weight is 201.7 g.

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Q. Question 18
The weight of coffee in 70 packets are shown in the following table

\begin{matrix} W e i g h t (i n g) & N u m b e r o f p a c k e t s 200 - 201 & 12 201 - 202 & 26 202 - 203 & 20 203 - 204 & 9 204 - 205 & 2 205 - 206 & 1 \end{matrix}

Determine the model weight.

Q. Question 4
The weights of tea in 70 packets are shown in the following table

\begin{matrix} Weight(in~g) & Number of packets 200 - 201 & 13 201 - 202 & 27 202 - 203 & 18 203 - 204 & 10 204 - 205 & 1 205 - 206 & 1 \end{matrix}

Find the mean weight of packets.

Q. The weight of coffee (in gm) in 70 packets is given below.

Weight(in gm)	200-201	201-202	202-203	203-204	204-205	205-206
No. of packets	12	26	20	9	2	1

Determine the modal weight of coffee in the packets.

Q. The weights of tea in 70 packets are shown in the following table:

Weight (in grams)	200−201	201−202	202−203	203−204	204−205	205−206
Number of packets	13	27	18	10	1	1

Find the mean weight of packets using step-deviation method. [CBSE 2013]

The weight of coffee in 70 jars is shown in the following table :

$\begin{matrix} Weight (in grams) : & 200 - 201 & 201 - 202 & 202 - 203 & 203 - 204 & 204 - 205 & 205 - 206 Frequency : & 13 & 27 & 18 & 10 & 1 & 1 \end{matrix}$

Determine the variance and standard deviation of the above distribution.

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Weight	200-201	201-202	202-203	203-204	204-205	205-206
Number of packets	12	26	20	9	2	1

Question 18 The weight of coffee in 70 packets are shown in the following table Weight 200-201 201-202 202-203 203-204 204-205 205-206 Number of packets 12 26 20 9 2 1Determine the model weight.

In the given data, the highest frequency is 26, which lies in the interval 201-202 Here, l=201fm=26,f1=12,f2=20 and (class width) h = 1 ∴ Mode =l+(fm−f12fm−f1−f2)×h⇒Mode=201+(26−122×26−12−20)×1 =201+(1452−32)=201+1420=201+0.7=201.7 g Hence, the modal weight is 201.7 g.

Question 18
The weight of coffee in 70 packets are shown in the following table
Weight
200-201
201-202
202-203 203-204 204-205 205-206
Number of packets
12 26 20 9 2 1

Determine the model weight.