To analyze the box plot provided in the image, let's evaluate the given options one by one.

1. Median of the data is necessarily equal to 37.5:

   • The median is represented by the line inside the box. From the box plot, the median appears to be around 37.5.

2. The interquartile range (IQR) of the given data is 25:

   • The IQR is the range between the first quartile (Q1) and the third quartile (Q3). From the plot, Q1 is around 25, and Q3 is around 50. Therefore, the IQR = Q3 - Q1 = 50 - 25 = 25.

3. There is no outlier in the dataset plotted in the box plot:

   • Outliers are typically shown as individual points outside the whiskers of the box plot. Since no individual points are displayed beyond the whiskers, there are no outliers.

4. Mode of the dataset will necessarily lie in [50, 55]:

   • The box plot does not provide direct information about the mode of the dataset. The mode is the most frequently occurring value, and this information cannot be determined from the box plot alone. Therefore, this statement cannot be confirmed as necessarily true.

Based on the analysis:

• The correct options are:
  • Median of the data is necessarily equal to 37.5
  • The interquartile range of the given data is 25
  • There is no outlier in the dataset plotted in the box plot

Do you want any more details or have any questions?

Here are 5 more questions you might ask:

1. How do you interpret a box plot?
2. What are quartiles and how are they calculated?
3. What is the difference between the median and the mean?
4. How can you identify outliers using a box plot?
5. What are some common uses of box plots in data analysis?

Tip: When interpreting box plots, always look at the length of the whiskers and the position of the median to understand the distribution and skewness of the data.