Math Problem Statement

At Noodle Factory Limited, the following data were collected every half an hour: X = Weight in gm. Data: [46, 37, 40, 33, 42, 36, 40, 47, 37, 35]. Calculate: (i) Mean, (ii) Median, (iii) Mode, (iv) Range, (v) Variance, (vi) Standard Deviation.

Solution

Here are the calculations based on the provided dataHere are the calculations based on the provided

  1. Mean: 39.3gm39.3 \, \text{gm}
  2. Median: 38.5gm38.5 \, \text{gm}
  3. Mode: 37gm37 \, \text{gm}
  4. Range: 14gm14 \, \text{gm} (difference between 47 and 33)
  5. Variance: 19.21gm219.21 \, \text{gm}^2
  6. Standard Deviation: 4.38gm4.38 \, \text{gm}

Would you like a deeper explanation or more details on any of these?

Here are some related questions for further exploration:

  1. What is the significance of variance in data analysis?
  2. How does the mode differ from the mean and median in interpreting data?
  3. Can the standard deviation alone determine data spread effectively?
  4. Why does the population variance use NN while sample variance uses N1N-1?
  5. How would these calculations differ if the data size was much larger?

Tip: A small standard deviation indicates that data points are close to the mean, while a large one suggests more spread out data.

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Math Problem Analysis

Mathematical Concepts

Descriptive Statistics
Central Tendency
Spread of Data

Formulas

Mean = (Sum of all data points) / (Number of data points)
Median = Middle value of the ordered data set
Mode = Most frequently occurring value in the data set
Range = Maximum value - Minimum value
Variance = Sum of squared differences from the mean / Number of data points
Standard Deviation = Square root of the variance

Theorems

Fundamental properties of statistical measures

Suitable Grade Level

Grades 9-10